Multiple crack weight for solution of multiple interacting cracks by meshless numerical methods

Muravin, Boris; Turkel, Eli

doi:10.1002/nme.1661

Cited by 22 publications

(18 citation statements)

References 26 publications

(35 reference statements)

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“…15. The computed SIF results are summarized and compared with three reference solutions, respectively from Daux et al (2000), Muravin and Turkel (2006), and Cheung et al (1984) in Table 3. From this table, the excellent accuracy can also be easily seen.…”

Section: A Symmetrically Branched Crack In a Finite Platementioning

confidence: 99%

“…Since elements are not involved any more, meshless methods avoid distortion or coincidence of elements with the crack geometries, and therefore are regarded as being more effective than the FEM in this respect Rao and Rahman 2000;Duflot and NauyenDang 2004). In particular, in the element-free Galerkin (EFG) method, as a representative, introduction of the moving least squares in the interpolation approximation is beneficial to evaluate the SIF and to model the crack growth (Belytschko et al 1994(Belytschko et al , 1995a(Belytschko et al ,b, 1996Krysl and Belytschko 1999;Muravin and Turkel 2006). However, as we know, the difficulties in the numerical integration and superimposition of essential boundary conditions are unavoidably encountered in this kind of methods (Strouboulis et al 2000a,b).…”

Section: Introductionmentioning

confidence: 97%

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Modeling complex crack problems using the numerical manifold method

Zhang

et al. 2009

Int J Fract

226

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In the numerical manifold method, there are two kinds of covers, namely mathematical cover and physical cover. Mathematical covers are independent of the physical domain of the problem, over which weight functions are defined. Physical covers are the intersection of the mathematical covers and the physical domain, over which cover functions with unknowns to be determined are defined. With these two kinds of covers, the method is quite suitable for modeling discontinuous problems. In this paper, complex crack problems such as multiple branched and intersecting cracks are studied to exhibit the advantageous features of the numerical manifold method. Complex displacement discontinuities across crack surfaces are modeled by different cover functions in a natural and straightforward manner. For the crack tip singularity, the asymptotic near tip field is incorporated to the cover function of the singular physical cover. By virtue of the domain form of the interaction integral, the mixed mode stress intensity factors are evaluated for three typical examples. The excellent results show that the numerical manifold method is prominent in modeling the complex crack problems.

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Section: A Symmetrically Branched Crack In a Finite Platementioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Modeling complex crack problems using the numerical manifold method

Zhang

et al. 2009

Int J Fract

226

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show abstract

“…Normalized stress intensity factors were calculated and compared to the analytical solution which was presented by [24] using meshless methods as a comparison to the analytical solutions given by [25,26] as illustrated in Table 5. As shown in this Table 5 the agreements are obviously excellent.…”

Section: Double Edge Notched Plate (Dent)mentioning

confidence: 99%

Finite Element Analysis of the Crack Propagation for Solid Materials

Souiyah

Muchtar²,

Alshoaibi

et al. 2009

American J. of Applied Sciences

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Problem statement:The use of fracture mechanics techniques in the assessment of performance and reliability of structure is on increase and the prediction of crack propagation in structure play important part. The finite element method is widely used for the evaluation of SIF for various types of crack configurations. Source code program of two-dimensional finite element model had been developed, to demonstrate the capability and its limitations, in predicting the crack propagation trajectory and the SIF values under linear elastic fracture analysis. Approach: Two different geometries were used on this finite element model in order, to analyze the reliability of this program on the crack propagation in linear and nonlinear elastic fracture mechanics. These geometries were namely; a rectangular plate with crack emanating from square-hole and Double Edge Notched Plate (DENT). Where, both geometries are in tensile loading and under mode I conditions. In addition, the source code program of this model was written by FORTRAN language. Therefore, a Displacement Extrapolation Technique (DET) was employed particularly, to predict the crack propagations directions and to, calculate the Stress Intensity Factors (SIFs). Furthermore, the mesh for the finite elements was the unstructured type; generated using the advancing front method. And, the global h-type adaptive mesh was adopted based on the norm stress error estimator. While, the quarterpoint singular elements were uniformly generated around the crack tip in the form of a rosette. Moreover, make a comparison between this current study with other relevant and published research study. Results: The application of the source code program of 2-D finite element model showed a significant result on linear elastic fracture mechanics. Based on the findings of the two different geometries from the current study, the result showed a good agreement. And, it seems like very close compare to the other published results. Conclusion: A developed a source program of finite element model showed that is capable of demonstrating the SIF evaluation and the crack path direction satisfactorily. Therefore, the numerical finite element analysis with displacement extrapolation method, had been successfully employed for linear-elastic fracture mechanics problems.

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“…Two single crack problems with different tractions applied to the crack which led to the Riemann-Hilbert problem were examined. Muravin and Turkel [5] designed a multiple crack weight (MCW) method for the strongly interacting cracks. They developed an algorithm for the construction of weight functions to handle multiple interacting cracks.…”

Section: Introductionmentioning

confidence: 99%

A Quadrature Approach for N-Collinear Crack Problem in an Orthotropic Strip

Yusufoğlu¹,

Çetinkaya²

2017

JMSS

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This study presents the determination of the stress intensity factors (SIFs) at the edges of the cracks in an elastic strip weakened by N-collinear cracks. The problem of an orthotropic elastic strip is reduced to a system of Cauchy type singular integral equations. The system of singular integral equations is approached by a Quadrature technique. Under two different loading conditions, the results are obtained for the different cases of crack numbers. The resistance of the strip is examined by considering the orthotropic properties of the strip material. Finally, the crack interactions are clarified during the analysis.

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Multiple crack weight for solution of multiple interacting cracks by meshless numerical methods

Cited by 22 publications

References 26 publications

Modeling complex crack problems using the numerical manifold method

Modeling complex crack problems using the numerical manifold method

Finite Element Analysis of the Crack Propagation for Solid Materials

A Quadrature Approach for N-Collinear Crack Problem in an Orthotropic Strip

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